Ocean Modelling 113 (2017) 131–144

Contents lists available at ScienceDirect

Ocean Modelling

journal homepage: www.elsevier.com/locate/ocemod

Assimilating Lagrangian data for parameter estimation in a

multiple-inlet system

L.C. Slivinski a , b , ∗, L.J. Pratt c , I.I. Rypina

c , M.M. Orescanin

d , B. Raubenheimer c , J. MacMahan

d , S. Elgar c

a Cooperative Institute for Research in Environmental Sciences (CIRES), Univ. of Colorado, Boulder, CO, USA b NOAA/Earth System Research Laboratory, Boulder, CO, United States c Woods Hole Oceanographic Institution, Woods Hole, MA, USA d Naval Postgraduate School, Monterey, CA, USA

a r t i c l e i n f o

Article history:

Received 27 October 2016

Revised 21 March 2017

Accepted 1 April 2017

Available online 5 April 2017

Keywords:

Data assimilation

Modelling

Drag coefficient

Drifters

Tidal inlets

a b s t r a c t

Numerical models of ocean circulation often depend on parameters that must be tuned to match either

results from laboratory experiments or field observations. This study demonstrates that an initial, subop-

timal estimate of a parameter in a model of a small bay can be improved by assimilating observations

of trajectories of passive drifters. The parameter of interest is the Manning’s n coefficient of friction in

a small inlet of the bay, which had been tuned to match velocity observations from 2011. In 2013, the

geometry of the inlet had changed, and the friction parameter was no longer optimal. Results from syn-

thetic experiments demonstrate that assimilation of drifter trajectories improves the estimate of n , both

when the drifters are located in the same region as the parameter of interest and when the drifters

are located in a different region of the bay. Real drifter trajectories from field experiments in 2013 also

are assimilated, and results are compared with velocity observations. When the real drifters are located

away from the region of interest, the results depend on the time interval (with respect to the full avail-

able trajectories) over which assimilation is performed. When the drifters are in the same region as the

parameter of interest, the value of n estimated with assimilation yields improved estimates of velocity

throughout the bay.

© 2017 Published by Elsevier Ltd.

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. Introduction

Bottom stress is important to circulation in shallow water, and

ts inclusion in numerical models can have significant impacts on

he simulation results. However, it is difficult to measure spatially-

arying bottom stress directly in the field ( Trowbridge et al., 1999;

anford and Lien, 1999; Biron et al., 2004 ), and thus often stress

s approximated with a bottom drag coefficient derived from lab-

ratory experiments or by tuning numerical model simulations

o observations, which usually involves iterations of model re-

ults that are time-consuming and costly ( Cheng et al., 1999; Chen

t al., 2015; Orescanin et al., 2016 ). Drag coefficients also can be

stimated from observations of the flow by assuming a balance

etween pressure gradients and bottom stress ( Feddersen et al.,

0 0 0; Seim et al., 20 02; Apotsos et al., 2008; Kim et al., 20 0 0;

rescanin et al., 2014 ). These coefficients have been estimated in

ther regions by assimilating sea-level data into numerical simu-

∗ Corresponding author.

E-mail address: laura.slivinski@noaa.gov (L.C. Slivinski).

m

(

2

ttp://dx.doi.org/10.1016/j.ocemod.2017.04.001

463-5003/© 2017 Published by Elsevier Ltd.

ations ( Mayo et al., 2014 ). Here, the Manning’s n drag coefficient

n a multiple tidal inlet system on Martha’s Vineyard, MA is esti-

ated by assimilating observed Lagrangian drifter trajectories into

numerical model for sea level and circulation.

Martha’s Vineyard is separated from Chappaquiddick Island by

atama Bay, which is connected to Vineyard Sound via Edgartown

hannel and to the Atlantic Ocean via the ephemeral Katama In-

et ( Fig. 1 A). Norton Point, the sand spit between the bay and the

tlantic, was breached by a storm in 2007 (yellow arrow, Fig. 1 B),

orming Katama Inlet. Over the following years, the inlet became

arrower, longer, and shallower as it migrated eastward ( Fig. 1 B,

), and friction became more important to sea level and circula-

ion in the bay ( Orescanin et al., 2016 ).

Data assimilation provides a framework for combining uncer-

ain estimates from numerical models with noisy observations to

stimate a variable that changes in time ( Kalnay, 2003 ). For geo-

hysical fluid flows, velocity fields and bathymetry can be esti-

ated by assimilating Eulerian observations from in-situ sensors

Madsen and Cañizares, 1999; Oke et al., 2002; Kurapov et al.,

005; Wilson et al., 2010 ) or Lagrangian observations from drifting

132 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

Fig. 1. A) Satellite image (Google Earth, 2012) of Katama Bay, Katama Inlet, and Edgartown Channel, with an inset showing the location of Katama Bay (red circle on Martha’s

Vineyard) relative to Boston and Cape Cod, B) Katama Inlet in 2011 showing the location of the initial breach of Norton Point (yellow arrow), and C) Katama Inlet in 2013

during drifter deployments. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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sensors ( Ide et al., 2002; Mariano et al., 2002; Molcard et al., 2005,

2006; Salman et al., 2006; Apte et al., 2008 ). Drifters follow (ap-

proximately) the motion of fluid parcels, and assimilation of their

trajectories leads to improved estimates of large-scale circulation

patterns ( Taillandier et al., 2006; Jacobs et al., 2014 ) and flows in

vortices ( Vernieres et al., 2011 ). Lagrangian observations also have

been assimilated in models that estimate the topography in a lab-

oratory channel ( Honnorat et al., 2010 ) and the bathymetry in a

river ( Landon et al., 2014 ). Synthetic experiments have compared

the Eulerian flow fields estimated by assimilating velocities de-

rived from Lagrangian data (so-called pseudo-Lagrangian data as-

similation) and by assimilating Lagrangian trajectories directly, and

the results show that the direct assimilation of trajectories outper-

forms pseudo-Lagrangian data assimilation ( Molcard et al., 2003 ).

In 2011, when Katama Inlet was open ( Fig. 1 B), current meters

were deployed throughout the bay ( Orescanin et al., 2014; 2016 ).

A numerical model (ADCIRC, Luettich and Westerink, 1991 ) of the

circulation in the bay at this time was developed, using boundary

conditions from pressure gauges deployed in 2011, and the Man-

ning’s n coefficient in the region of Katama Inlet was tuned to

match the data from the current meters in 2011. In 2013, after the

inlet had begun to migrate and narrow ( Fig. 1 C), current meters

were again deployed throughout the bay. Results from the numer-

ical model using boundary conditions from the gauges deployed

in 2013, but with the same estimates of Manning’s n from 2011,

were compared with the 2013 observations from the current me-

ters. Orescanin et al. (2016) found that discrepancies between the

2013 observations and the numerical model were due to changes

in friction, and therefore, the value of Manning’s n in Katama In-

let estimated from 2011 data was suboptimal when modeling the

2013 system.

Here, drifter tracks observed in the Katama Bay system are

assimilated into a numerical circulation model (ADCIRC) to esti-

mate the bottom friction. The model uses bathymetry measured

throughout the system and is driven with observed tides, and sim-

ulations with and without assimilating drifter data are compared

with Eulerian observations of currents in Katama Bay. As a proof

of concept, synthetic observation experiments are performed first.

Experiments assimilating real drifter data are performed next. Re-

sults from assimilating synthetic and real drifter trajectories in two

distinct regions of Katama Bay are compared.

2. Numerical model and observations

2.1. Numerical model of Katama Bay

Sea level and depth-averaged currents in Katama Bay are sim-

ulated with the two-dimensional version of the Advanced Circula-

ion Model (ADCIRC, Luettich and Westerink, 1991 ), which solves

version of the shallow water equations via a finite-element

ethod. This model assumes no stratification in the domain; this

as supported by observations in Katama Bay. Casts from CTD

conductivity, temperature, depth) instruments throughout the sys-

em show little to no temperature or salinity stratification. Within

he bay, the depths are very shallow, so this is expected. Offshore

n Vineyard Sound and the Atlantic, in depths less than 10 m, the

ame lack of vertical structure was observed. Winds were light ( <

m/s) and waves were small ( < 1 m) during the drifter deploy-

ent periods, and are not included here. The numerical grid con-

ists of a finite-element triangular mesh with spacing ranging from

0 min the inlets and 15 min the bay to 200 m outside the

nlets in both the Atlantic Ocean and Vineyard Sound ( Fig. 2 A).

athymetry (5 to 20 m horizontal and 0.05 m vertical resolu-

ion) in the bay, the inlets, and the ebb tidal delta ( Fig. 2 A) was

easured in 2013 with GPS and an acoustic altimeter mounted

n a personal water craft, and interpolated onto the model grid

Orescanin et al., 2016 ). Pressure gauges and current meters were

o-located at ten locations within Edgartown Channel, Katama

ay, and Katama Inlet (orange circles in Fig. 3 ) ( Orescanin et al.,

016 ). The northern boundary of the model is forced with the sea-

evel observations in Edgartown Harbor (yellow circle in Fig. 2 A),

nd the southern boundary is forced with observations from the

artha’s Vineyard Coastal Observatory (12 m depth, 4 km west

f Katama Inlet; not shown).

To estimate quadratic bottom stress, the model converts bot-

om roughness given by a user-defined value of Manning’s n (units

/m

1/3 ) at each node to an equivalent quadratic drag coefficient

iven by:

d (t) =

gn

2

( D + η(t) ) 1 / 3

, (1)

here g is gravity, t is time, D is the local mean depth, and

( t ) is the water surface elevation above D ( Luettich and West-

rink, 1991 ).

The Katama Bay domain is divided into several subregions

ased on bathymetry, each with a different value of Manning’s n

see Fig. 2 B.) In the original 2011 simulations, the deep boundary

egions (dark blue in Fig. 2 B) outside of the bay were assigned the

alue n = 0 . 020 s/m

1 / 3 , which is standard for open water. The bay

light blue) was assigned n = 0 . 030 s/m

1 / 3 , which was calculated

y converting the bottom stress estimated from a pressure gradient

alance ( Orescanin et al., 2014 ) into n using an average depth of

he bay. However, model-data comparisons ( Orescanin et al., 2016 )

uggested that the friction coefficient needed to be increased to

= 0 . 035 s/m

1 / 3 in an area surrounding Katama Inlet (green area

n Fig. 2 B) in 2011. This spatial and temporal variation in n is

L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144 133

Fig. 2. A) Google Earth image of the Katama system with seafloor and land elevation contours (colors, scale on right), the grid mesh, and the Edgartown Harbor pressure

gauge (yellow circle) and B) the bathymetrically-defined subregions with different friction factors ( n ; values for the colors are given in the legend, units s/m

1/3 ). (For

interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 3. Trajectories of real drifters deployed August 20, 2013 for approximately

140 min (Channel Trajectories) and August 22, 2013 for approximately 110 min (In-

let Trajectories) in Katama Bay. Orange circles are locations of acoustic Doppler cur-

rent meters (water depths < 2 m) and profilers (depths > 2 m). (For interpretation

of the references to colour in this figure legend, the reader is referred to the web

version of this article.)

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ue mainly to changes in bedforms; for example, sand waves and

unes were observed throughout the system, and tended to mi-

rate over time. These values of Manning’s n are typical in tidal in-

ets, including multiple tidal inlet systems ( Mehta and Joshi, 1998;

raus and Militello, 1999; Friedrichs and Madsen, 1992; Friedrichs,

995; Dias et al., 2009 ).

By iteratively simulating the 2011 circulation, Manning’s n

as estimated as the value that minimized the difference be-

ween observed and simulated kinetic energy in the bay circu-

ation ( Orescanin et al., 2016 ). The tuning required several dif-

erent model simulations, as well as a method for determining

hich value is optimal, because varying n can improve kinetic en-

rgy estimates in the inlet while degrading estimates elsewhere

n the bay. For the estimation of the 2011 circulation, the root

ean squared errors between the simulated and observed ve-

ocity kinetic energies, tidal currents, and sea-level amplitudes

nd phases were minimized. In particular, n was tuned until

he errors at each of the seven observation locations were less

han 15%, while minimizing the total error throughout the do-

ain ( Orescanin et al., 2016 , especially Table 1). The Katama Inlet

athymetry changed substantially between 2011 and 2013 (com-

are Fig. 1 C with 1 B), and simulations using the 2013 bathymetry

nd the 2011-estimated n had decreased skill within Katama Inlet

Orescanin et al., 2016 ). Note also that the flow has the greatest

elocities in the inlet, and therefore changes in n here have large

ffects throughout the system ( Orescanin et al., 2016 ). Here, La-

rangian drifter data from 2013 field experiments are assimilated

nto the model to improve the estimates of friction in Katama Inlet

n 2013.

.2. Drifter observations in 2013

In August 2013, several drifter deployments were conducted

ith twelve drifters released in multiple deployments over sev-

ral days. On August 20, the drifters targeted Edgartown Channel,

nd on August 22, they targeted Katama Inlet ( Fig. 3 ). The surface

racking drifters used herein are a modified version of drifters de-

loyed in the surf zone ( MacMahan et al., 2009; Fiorentino et al.,

012 ) and rivers ( Landon et al., 2014 ), both in body shape and

ype of handheld GPS. These drifters were deployed together in

he inner shelf and visually behaved similarly. The GPS used on

he 2013 Katama drifters is a Locosys GT-31, which provides ac-

urate relative position useful for velocity measurements. The Lo-

osys GPS has successfully measured surfzone velocities and tra-

ectories ( McCarroll et al., 2014 ) and surface gravity wave eleva-

ions ( Herbers et al., 2012 ). The inlet drifters were also deployed

s part of an experiment in the inner shelf of the Gulf of Mexico.

he drifter trajectories compared well to acoustic Doppler current

134 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

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Fig. 4. Synthetic drifter trajectories in Katama Bay. Thin white trajectories are from

the drifters released on model date August 20 in Edgartown Channel, and thick

white trajectories are from drifters released on model date August 22 just outside

Katama Inlet.

profiler (ADCP) surface velocity estimated trajectories ( Roth et al.,

2017 ).

3. Overview of Lagrangian data assimilation

Lagrangian data can be assimilated directly or indirectly. In

pseudo-Lagrangian data assimilation ( Molcard et al., 2003 ), se-

quential positions of the drifters are converted to Lagrangian veloc-

ities, which are then assimilated into the model. Fully Lagrangian

data assimilation uses the positions of the drifters directly, such

as in the augmented vector approach ( Kuznetsov et al., 2003 ), in

which the positions of the drifters are appended to the state vector

at each time step. With this approach, to assimilate observations of

a single drifter following the flow into a two-dimensional velocity

field, the augmented vector at time t is [ u, v, x, y ]( t ), where u and v

are a representation of the velocity field at each model grid point

at time t , and ( x, y ) is the position of the drifter at that time.

Here, the focus is on estimating n as a parameterization of

the flow field, so the state vector is [ n, x 1 , y 1 , . . . x N D , y N D ] for N D

drifters. The velocity [ u, v ] is not estimated directly from the as-

similation, and thus does not appear in the state vector, although

the evolution of the drifter positions depends on the time-variable

velocity field, which depends on n .

3.1. Ensemble Kalman filter

The data assimilation method used here is the ensemble

Kalman filter (EnKF) ( Evensen, 1994 ), which is used both oper-

ationally ( Wei et al., 2006 ) and in test problems, including La-

grangian data assimilation ( Salman et al., 20 06, 20 08 ). The EnKF

assimilates consecutive observations serially. At each time step, the

best estimate and a quantification of its uncertainty are provided

by an ensemble of possible realizations. When an observation is

available, the ensemble is updated to reflect the new information.

Here, the EnKF is reviewed briefly in the context of Lagrangian data

assimilation for parameter estimation.

Let the state vector be given by z (t) =[ n, x 1 (t) , y 1 (t) , . . . x N D (t) , y N D (t)] . At times t 1 , t 2 , . . . t f drifters

are observed at positions q obs , so that

q obs (t k ) = H z (t k ) + εk (2)

where H = [0 I ] is the observation operator in the augmented vec-

tor setup, and εk ∼ N (0 , R ) where R is the observational error co-

variance. The observation errors are assumed to be uncorrelated in

time, independent, and Gaussian so that R = σ 2 R I is diagonal.

Assume that at time t k −1 , there is an ensemble { z i (t k −1 ) } for

i = 1 . . . N e , and the next available observation is at time t k . The

forecast ensemble is computed by evolving each ensemble member

forward under the dynamics. Although the parameter being esti-

mated could evolve under a dynamic model as well, here the pa-

rameter remains the same between observation times, but the flow

determined by that parameter evolves according to the numerical

model (in this case, ADCIRC.) Each ensemble member’s drifters si-

multaneously are advected passively under that velocity field, giv-

ing the forecast ensemble at time t k , { z f i (t k ) } , which will be up-

dated to reflect the observation. The EnKF update step, also known

as the analysis step, is applied to each ensemble member according

to:

z a i = z f i

+ P

f H

T (H P

f H

T + R

)−1 (H z f

i − [ q obs + ηi ]

)(3)

P

f =

1

N e − 1

N e ∑

i =1

(z f

i − z

f )(

z f i

− z f )T

where P

f is the sample covariance of the forecast ensemble and

ηi ∼ N (0 , R ) for the perturbed observation formulation of the

EnKF ( Evensen, 2003 ). This step takes place entirely at time t , and

k

hus the time dependence has been dropped. The forecast-analysis

ycle is then repeated for each available consecutive observation

ime.

Here, the scalar Manning’s n in the Katama Inlet area (green

egion in Fig. 2 ) is estimated using drifter trajectories located

hroughout the bay. Thus, only n and the drifter positions are up-

ated at each analysis step; in the forecast step, the full velocity

nd elevation fields of the entire domain evolve according to AD-

IRC with the latest updated value of n in Katama Inlet.

.2. Observing system simulation experiments

The method is tested in an artificial scenario known as an ob-

erving system simulation experiment (OSSE), in which the same

odel used in the forecast step of the assimilation method also is

sed to create a synthetic truth consisting of time series of both

he velocity field and the drifter positions. Random (Gaussian) per-

urbations are then added to the true drifter trajectories to simu-

ate noisy observations. An initial ensemble of the flow and drifters

s generated by perturbing the true initial value of Manning’s n in

atama Inlet and the true drifter positions. This yields an ensemble

f different flow states, each consistent with a perturbed value of

, and each with different initial drifter positions. The performance

f the data assimilation method is then judged based on its abil-

ty to recover the true value of n in the inlet from the perturbed

nitial ensemble and the noisy observations.

Two OSSEs are run. One assimilates drifter trajectories from

atama Inlet (thick white curves in Fig. 4 ), and the other assim-

lates trajectories from Edgartown Channel, located north of the

nlet subdomain (thin white curves in Fig. 4 ). The drifter release

imes and locations are designed to mimic the real data avail-

ble from August 2013. In both experiments, the synthetic truth

s a 6 h time series of the velocity field generated with Manning’s

= 0 . 035 s/m

1 / 3 in the inlet and the trajectories from 13 drifters.

he initial ensemble of drag coefficients { n i } for i = 1 . . . N e = 30

s drawn from a normal distribution with mean 0.025 s/m

1/3 and

tandard deviation 0.005 s/m

1/3 . This is a common ensemble size

or this size problem ( Houtekamer and Mitchell, 2001; Mitchell

t al., 2002; Evensen, 2003 ). Decreasing the ensemble size to N e =0 degrades the performance, but N e = 20 yields similar results as

e = 30 . In practice, some a priori knowledge of the feasible range

L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144 135

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f values is necessary in order to choose the initial ensemble mean

nd spread. For the synthetic experiments here, the initial ensem-

le is defined relatively far from the truth (the mean is two stan-

ard deviations less than the true value of n ) to determine whether

he assimilation can recover the truth even under these conditions.

The observation error of the drifters has mean 0 and standard

eviation σR = 25 m. This is larger than the value of approximately

m given by MacMahan et al. (2009) as the error of the real

rifter positions, to prevent the assimilation ensemble from col-

apsing onto the observations too quickly and resulting in filter

ivergence. Here, “filter divergence” refers to the collapse of the

nsemble onto the incorrect estimate of n , but it could also re-

ult in an estimate of the uncertainty surrounding n that is not

arge enough (due to an ensemble spread that is too small). Fil-

er divergence is often a result of applying an approximately lin-

ar method (that is, the EnKF) to a nonlinear problem (such as

rifter trajectories in a nonlinear flow) and has been demonstrated

n the Lagrangian data assimilation setup ( Apte et al., 2008; Slivin-

ki et al., 2015 ). In a system that has only weakly nonlinear char-

cteristics, the EnKF can avoid divergence if larger errors are in-

luded ( Mitchell et al., 2002 ). Although overestimating observation

rror can potentially have detrimental effects, such as increasing

he time it takes for the ensemble estimate to converge and pro-

iding an artificial lower bound on the errors in the estimates,

he results in the following section suggest that the assimilation

orked well with the chosen values: the ensemble does not col-

apse too early nor does it diverge. The time between subsequent

bservations �t is tested for �t = 1, 5, and 10 min. The veloc-

ig. 5. Ensemble (thin light red curves) and mean (thick red curves) estimates for Mannin

nlet, for �t = (A) 1, (B) 5, and (C) 10 min. The black line is n = 0 . 035 s/m

1 / 3 . (For inter

he web version of this article.)

ty fields for both the synthetic truth and the initial ensemble are

pun up with their respective values of n for several days, so that

ll the simulations have reached equilibrium before assimilation

egins.

. Results from synthetic experiments

.1. Drifters within the subdomain of interest

OSSEs are run with drifters released just outside Katama Inlet

hen the flow is from south to north into the inlet, through the

ay, and out through Edgartown Channel to Vineyard Sound. The

rifter deployment times and locations are chosen to mimic the

eal observations, so N D = 13 synthetic drifters are released (in the

umerical model) just outside the inlet starting at 8:30 am (EDT)

ugust 22, 2013. To study the convergence of the estimates of n ,

he data are assimilated over a period of 6 h, significantly longer

han the 1–2 h-long time windows of the real drifter observations.

For each of the �t , the assimilation estimates n fairly well, con-

erging after about 60 min ( Fig. 5 ). However, for �t = 10 min,

he assimilation initially overestimates n slightly, and gradually de-

reases to the truth over the six hour window ( Fig. 5 C).

The estimates of kinetic energy, defined as 0.5 times the sum of

quared velocity over all grid points i : 1 2

∑

i (u 2 i

+ v 2 i ) for the three

ata assimilation experiments, also converge within 60 min to the

ynthetic true values ( Fig. 6 (A–C)). A “free run”, in which the ini-

ial ensemble members are each integrated forward without assim-

lation for 6 h with the initial value of n remaining constant, has

g’s n versus assimilation time on August 22, when drifters were released in Katama

pretation of the references to colour in this figure legend, the reader is referred to

136 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

Fig. 6. Ensemble (thin light red curves) and mean (thick red curves) estimates of kinetic energy versus assimilation time on August 22, when drifters were released in

Katama Inlet, for �t = (A) 1, (B) 5, and (C) 10 min, as well as the case with no data assimilation (D). The black curves are the synthetic “truth” from the simulation with

n = 0 . 035 s/m

1 / 3 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

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poorer performance than the assimilation runs (compare Fig. 6 D

with A–C). These results demonstrate that changing the friction

(via assimilation) on these time scales has near-immediate effects

on the total kinetic energy in the model, and thus, the assimilated

ensemble predicts the correct kinetic energy as quickly as it esti-

mates the correct value of the drag coefficient.

4.2. Drifters in Edgartown Channel

Three additional experiments are run with the same setup as

above, but with the drifters released in Edgartown Channel. Again,

the deployment time (10:40 am August 20, 2013) and initial loca-

tions of the 13 drifters are chosen to match the real data, and ob-

servations are assimilated for six hours for �t = 1, 5, and 10 min.

Although the drifters never approach the inlet subdomain in which

the drag coefficient is estimated, the assimilation converges to the

correct “true” value of n ( Fig. 7 ). However, assimilating drifters in

Edgartown Channel results in a longer time to convergence than

assimilating drifters in the inlet. For �t = 1 min, the ensemble

takes about 90 min to converge onto the truth ( Fig. 7 A), and for

�t = 10 min, it takes about 2 h ( Fig. 7 C). For �t = 5 min, the en-

semble initially diverges from the truth, and takes approximately

6 h to converge ( Fig. 7 B). This is likely due to a combination of

nonlinearity and random noise that has a stronger effect on the

assimilation when the observations are farther away from the re-

ion of interest, and is discussed below in more detail. Similar to

he releases in Katama Inlet ( Fig. 6 ), assimilation estimates of the

inetic energy converge to the true values at the same rate as n

onverges ( Fig. 8 ).

.3. Discussion

As expected, the assimilation of drifters in the same spatial lo-

ation (Katama Inlet) as the estimated n leads to quicker conver-

ence to the true n than the assimilation of drifters in Edgartown

hannel. This is consistent with the results of Salman et al. (2008) ,

ho showed that local structures within a flow field are well-

pproximated when the drifters stay close to those structures (eg,

hen the drifters are trapped in a vortex), whereas global flow

roperties are estimated best when the drifters cover most of the

omain (eg, when the drifters are spread out and some follow a jet

tream in the flow). Therefore, the performance of the Lagrangian

ata assimilation algorithm will depend on the spatial location of

he drifters and their trajectories.

Although the performance degrades slightly when the time be-

ween observations of drifters in Katama Inlet is increased, the as-

imilation estimates the correct value of n within about an hour

or each �t . Conversely, when drifters in Edgartown Channel are

ssimilated, the performance of the assimilation depends more

L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144 137

Fig. 7. Ensemble (thin light red curves) and mean (thick red curves) estimates of Manning’s n versus assimilation time on August 20, when drifters were released in

Edgartown Channel, for �t = (A) 1, (B) 5, and (C) 10 min. The black line is n = 0 . 035 s/m

1 / 3 . (For interpretation of the references to colour in this figure legend, the reader

is referred to the web version of this article.)

s

m

r

t

c

a

i

r

m

t

T

n

d

w

s

d

fi

a

i

p

s

o

a

o

s

1

i

p

r

d

t

a

s

n

1

c

t

b

t

c

c

0

a

trongly on the time between observations, and does not improve

onotonically as the time between observations decreases.

To determine why assimilating trajectories from Katama Inlet

esults in significantly faster convergence than assimilating Edgar-

own Channel trajectories, especially for intermediate �t = 5 min,

onsider the time it takes the kinetic energy in the bay to adjust

nd equalize after an abrupt change in the drag coefficient in the

nlet. A crude approximation of the adjustment time is the time

equired for a long gravity wave to propagate over the largest di-

ension of the bay l max in water depth d , and for a reflected wave

o return to the source over the same path:

adjustment ≈ 2

(

l max √

gd

)

(4)

≈ 2

(2 × 10

3 m

(9 . 8 ∗ 4) 1 / 2 m/s

)≈ 600 s.

Thus, the intrinsic time for Katama Bay to adjust to changes in

in the inlet is approximately 10 min.

To determine how long it takes the velocity field and the

rifters to adjust to the new value of Manning’s n , the system

as run for 4 days with n = 0 . 035 s/m

1 / 3 in the inlet and con-

tant north-to-south tidal forcing, similar to the case when the

rifters are released in Edgartown Channel. At the beginning of the

fth day, simulations with n = 0 . 01 , 0 . 02 , 0 . 03 , 0 . 035 , 0 . 04 , 0 . 05 ,

nd 0.06 s/m

1/3 were run. In each experiment, drifters are released

n Edgartown Channel at the same locations as the synthetic ex-

eriment above. Each situation is simulated for 1 hr, with no as-

imilation.

For a range of initial values of n , the kinetic energy averaged

ver the entire domain converges about 25 min after n is changed,

lthough for the simulations with the largest and smallest values

f n , the kinetic energy oscillates slowly ( Fig. 9 ). A change of 0.005

/m

1/3 in n from the true values results in convergence after about

0 min. Changing n by 0.025 s/m

1/3 results in about a 50% change

n kinetic energy (e.g., compare the blue ( n = 0 . 010 ) with the pur-

le ( n = 0 . 035 ) curve and compare the purple ( n = 0 . 035 ) with the

ed ( n = 0 . 060 ) curve in Fig. 9 ).

For the first 10 min after the change, the average speed of the

rifters released in Edgartown Channel does not depend on the ini-

ial value of n ( Fig. 10 ). The model simulates drifter advection with

4th order Runge–Kutta scheme with a 1 min time step, and the

imulations suggest that changes in the friction in Katama Inlet do

ot have an effect on the drifters in Edgartown Channel for at least

0 min, consistent with Eq. (4) .

It is unsurprising, then, that the assimilation takes longer to

onverge when the drifter observations are located in the channel

han when they are in the inlet: information takes longer to travel

etween Katama Inlet and Edgartown Channel than it does within

he inlet. Due to the nature of the data assimilation method, which

ombines uncertain forecasts with the noisy observations, the in-

rement made to n at each analysis step is generally no more than

.005 s/m

1/3 . In this regime, there is very little effect on the aver-

ge drifter speed before fifteen minutes, so the assimilated drifter

138 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

Fig. 8. Ensemble (thin light red curves) and mean (thick red curves) estimates of kinetic energy versus assimilation time on August 20, when drifters were released in

Edgartown Channel, for �t = (A) 1, (B) 5, and (C) 10 min, as well as the case with no data assimilation (D). The black curves are the synthetic “truth” from the simulation

with n = 0 . 035 s/m

1 / 3 . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 9. Kinetic energy spatially averaged over the entire domain versus time for different initial values of n (colors in the legend; units s/m

1/3 ) in the inlet. (For interpretation

of the references to colour in the text, the reader is referred to the web version of this article.)

L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144 139

Fig. 10. Average speed of 13 drifters released in Edgartown Channel versus time for different initial values of n (colors in the legend) in the inlet. (For interpretation of the

references to colour in this figure legend, the reader is referred to the web version of this article.)

t

s

e

a

d

s

o

a

i

s

w

e

n

�

t

�

w

i

n

o

t

s

r

s

n

t

5

5

A

A

m

t

o

t

o

e

s

n

a

a

(

a

I

t

2

I

m

o

o

i

0

s

s

n

s

a

p

t

A

2

w

v

1

w

T

t

f

rajectories will likely not reflect the changes in n within one as-

imilation step of any size studied here. Therefore, small differ-

nces in realizations of noise (in the drifter observations) could

ffect the timescale of convergence of n fairly strongly when the

rifters are in the channel.

To this end, experiments identical to the ones earlier in this

ection are run (results not shown), but with different realizations

f observation noise, sampled from the same Gaussian distribution

s the previous experiment. The second experiment with drifters

n Katama Inlet performs almost identically to the inlet experiment

hown above: the ensemble has converged onto the true value

ithin an hour, with the best performance for �t = 1 min. How-

ver, the experiment that assimilates drifters in Edgartown Chan-

el produces fairly different results from the experiment above. For

t = 1 min and �t = 5 min, the ensembles each take about 4 h

o converge, more than twice the time for the experiment with

t = 1 min above, but significantly less time than the experiment

ith �t = 5 min above. The experiment with �t = 10 min results

n about a 2.5 h convergence time for the second realization of

oise, as compared to the convergence time of 90 min for the

riginal experiment in Section 4.2 (see Fig. 7 .) This suggests that

he performance of the Edgartown Channel experiments depends

trongly on the realizations of observation noise. Ultimately, these

esults are likely due to subtle interactions between the effects de-

cribed here; this is typical in data assimilation experiments with

onlinear systems, which often arise in Lagrangian data assimila-

ion.

. Results from a field experiment

.1. Setup

The trajectories of surface drifters released in Katama Inlet on

ugust 22 (Inlet Trajectories in Fig. 3 ) and in Edgartown Channel

ugust 20 (Channel Trajectories in Fig. 3 ) are assimilated to esti-

ate the friction in Katama Inlet. Prior to reviewing the results of

he assimilation, the performance of the model is tested with the

riginal value n = 0 . 035 s/m

1 / 3 . The simulated kinetic energy from

hat experiment in the inlet is compared with the kinetic energy

bserved at 10 locations in the system ( Fig. 11 ). The model kinetic

nergy at each sensor location is calculated by interpolating the

imulated velocity between nearby grid points. The observed ki-

etic energy is calculated from currents measured about 0.8 m

bove the seafloor in water depths < 2 m and from a depth aver-

ge of the nearly uniform-in-the-vertical profiles in depths > 2 m

Orescanin et al., 2014 ).

The largest discrepancies between simulations with n = 0 . 035

nd observations are at locations 05 and 46, both close to Katama

nlet ( Fig. 3 ). The value n = 0 . 035 s/m

1 / 3 was based on observa-

ions in 2011, but the inlet lengthened, narrowed, and shoaled by

013, resulting in a significant change in n ( Orescanin et al., 2016 ).

nstead of re-tuning n with the 2013 in-situ observations, n is esti-

ated by assimilating drifter trajectories into the model.

Two experiments are performed – the first assimilates drifter

bservations in Katama Inlet, and the second assimilates drifter

bservations in Edgartown Channel. The model ensemble is initial-

zed with a mean of n = 0 . 035 s/m

1 / 3 and a standard deviation of

.005 s/m

1/3 . The observation error is set at σR = 25 m, as in the

ynthetic experiments.

Drifter data are available every second, but results from the

ynthetic runs ( Section 4 ) suggest that this is more frequent than

ecessary since assimilating data every 1 min was sufficient for

uccessful estimation in those experiments. Additionally, the EnKF

ssumes that observation errors are uncorrelated in time; if drifter

ositions are sampled every 1 sec, it is not clear that this assump-

ion will hold. Thus, �t = 1 . 0 min for the channel drifter data on

ugust 20, and �t = 0.5 min for the inlet drifter data on August

2 due to the shorter trajectories ( Fig. 3 ). Synthetic experiments

ith �t = 0 . 5 min for the inlet drifters (not shown) demonstrate

ery similar results to those with �t = 1 . 0 min.

On August 20, ten drifters were deployed in the channel at

0:50 am and recovered at 1:10 pm. On August 22, the drifters

ere deployed in several relatively short releases in the inlet.

welve drifters are assimilated from 8:31 until 8:48 am (Assimila-

ion Round 1), at which point each ensemble member is evolved

orward until 9:12 am with the final estimate of friction from

140 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

0

0.05Mooring 03

0

0.05Mooring 04

0

0.5

1Mooring 05

00.010.02

Mooring 41

Kin

etic

Ene

rgy

(m/s

)2

0

0.02

0.04Mooring 42

0

0.05

Mooring 43

0

0.05Mooring 44

00.10.2

Mooring 45

dateAug 20 Aug 21 Aug 22 Aug 23

0

0.1

0.2Mooring 46

dateAug 20 Aug 21 Aug 22 Aug 23

0

0.2

0.4Mooring 47

assimilation windowobservationsmodel

Fig. 11. Observed (solid black curves) and simulated (dashed blue curves, n = 0 . 035 ) kinetic energy versus time for 3 days in 2013. The shaded boxes are times during which

drifters were deployed. The location of each comparison is given by the mooring number at the top of each panel, which corresponds to a sensor on the map in Fig. 3 . Note

differences in scales of y-axes. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

08:30 08:45 09:00 09:15 09:30 09:45 10:00 10:15 10:30 10:45 11:00

time

0.025

0.03

0.035

0.04

0.045

0.05

Man

ning

s n

(s/m

1/3)

Analysis ensemble (real drifters), Aug 22 (inlet)

assim windowensemblemeaninitial estimate

Fig. 12. Ensemble (thin light red curves) and mean (thick red curves) estimates of Manning’s n from assimilating drifters within Katama Inlet versus time, with the initial

estimate of n = 0 . 035 s/m

1 / 3 (black horizontal line, the value found for the 2011 data ( Orescanin et al., 2016 )). Blue shaded regions are assimilation windows and unshaded

regions are time periods in which the ensemble estimates of n were kept constant. (For interpretation of the references to colour in this figure legend, the reader is referred

to the web version of this article.)

t

s

e

i

a

K

t

s

m

l

s

d

Round 1. At 9:12 am, the next wave of ten drifters are assimi-

lated for 10 min (Round 2). In Round 3, nine drifters are assim-

ilated from 9:42 until 9:47am, and in Round 4, nine drifters are

assimilated from 9:59 until 10:20 am. Note that the number of

drifters assimilated in each round is not constant, because not ev-

ery drifter was released at the exact same time nor did they all

provide meaningful trajectories. Thus, only drifters that provided

trajectories during overlapping time windows are assimilated.

5.2. Results and discussion

Manning’s n estimated by assimilating the Inlet Trajectories

converges to n = 0 . 045 s/m

1 / 3 ( Fig. 12 ), higher than the 2011 es-

imated value of 0.035 s/m

1/3 ( Orescanin et al., 2016 ). Without as-

imilation and with n = 0 . 035 , the model over-predicts the kinetic

nergy at almost every in-situ sensor location ( Fig. 13 ). By assim-

lating drifter data, the model is closer to the in-situ observations

t most locations, especially at sensors 05 and 47, located close to

atama Inlet ( Fig. 3 ). Specifically, since the observed drifters are

raveling more slowly than the simulated drifters within the as-

imilation, the EnKF analysis increases the drag coefficient to di-

inish the mismatch between the observed drifters and the simu-

ated drifters.

Figs. 12 and 13 show how the estimate of n and the as-

ociated kinetic energy change during assimilation, as n is up-

ated. In addition, another simulation is restarted on August 20

L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144 141

Fig. 13. Kinetic energy versus time for observations (black curves), the model with no assimilation and n = 0 . 035 s/m

1 / 3 (dashed blue curves), and ensemble (thin light red

curves) and mean (thick red curve) estimates of n from assimilating drifters within Katama Inlet on August 22 versus time at each sensor location (numbers on top of each

panel refer to sensor locations in the map in Fig. 3 ). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this

article.)

a

0

e

a

l

K

a

e

b

R

R

o

w

e

n

M

d

a

i

t

U

o

u

s

t

n

t

Table 1

Normalized root mean squared error of kinetic

energy between model simulations with given n

(units s/m

1/3 ) and the in-situ observations between

August 20 and 22.

Sensor n = 0 . 035 n = 0 . 018 n = 0 . 045

03 0.007 0.013 0.007

04 0.006 0.012 0.005

05 0.371 0.888 0.234

41 0.003 0.003 0.004

42 0.005 0.013 0.004

43 0.014 0.042 0.007

44 0.007 0.014 0.006

45 0.035 0.105 0.025

46 0.100 0.096 0.095

47 0.067 0.179 0.045

o

m

i

A

o

u

h

m

(

t

i

b

c

t

nd run for three full days with the final estimated value of n = . 045 s/m

1 / 3 . Model skill is quantified by the root mean square

rror (RMSE, averaged over August 20–22) in kinetic energy rel-

tive to that observed with the in-situ sensors. At each sensor

ocation, the observed kinetic energy at time t is calculated as

E obs (t) = 1 / 2 (u obs (t) 2 + v obs (t) 2

)for u obs , v obs observed latitudinal

nd meridional current velocities, respectively. Similarly, the mod-

led kinetic energy KE sim

(t) = 1 / 2 (u sim

(t) 2 + v sim

(t) 2 )

is calculated

y interpolating the simulated velocity to the sensor locations. The

MSE is defined as

MSE =

( ∑ t f t= t 0 ( KE obs (t) − KE sim

(t) ) 2

∑ t f t= t 0 ( KE obs (t) )

2

) 1 / 2

(5)

ver the time period from t 0 to t f . Relative to the simulation

ith n = 0 . 035 s/m

1 / 3 , the simulation with the assimilated param-

ter n = 0 . 045 s/m

1 / 3 yields improved kinetic energy estimates at

early every mooring, with the most significant improvement at

ooring 05, in Katama Inlet ( Table 1 ).

In contrast, the estimate of n in Katama Inlet from assimilating

rifter trajectories in Edgartown Channel does not converge, and

t the end of the time window n = 0 . 018 s/m

1 / 3 ( Fig. 14 ), signif-

cantly lower than the value estimated by assimilating drifters in

he inlet, and lower than the initial estimate of n = 0 . 035 s/m

1 / 3 .

nlike at the time of the Katama Inlet drifters’ release, at the time

f the drifters’ release in Edgartown Channel the model simulation

nderestimates the observed kinetic energy at 7 of the 10 in-situ

ensors ( Fig. 15 ). In particular, the original model underestimates

he kinetic energy at sensors 03, 04, and 41 in Edgartown Chan-

el (see Fig. 3 for locations), where the drifters were released, al-

hough the kinetic energy at sensor 42 (also near the channel) is

verestimated. The assimilation seeks to diminish this initial mis-

atch between the observed and simulated drifter trajectories by

ncreasing the kinetic energy via decreasing the drag coefficient.

s a result, towards the end of the assimilation period, both the

riginal simulation with n = 0 . 035 s/m

1 / 3 and the assimilated sim-

lations overestimate the observed kinetic energy ( Fig. 15 ).

The model run with the final value of n = 0 . 018 s/m

1 / 3 has

igher RMSE relative to the observed kinetic energy than the

odel using n estimated by assimilating drifters in the inlet

Table 1 ), with the biggest errors at sensor 05 in the inlet. To test if

he initial discrepancy in kinetic energy is indeed a driving factor

n the results of the assimilation, channel drifters are assimilated

eginning at 12:00 pm (rather than at 10:50 am), when the model

hanges from underestimating the observed kinetic energy to ei-

her overestimating or accurately estimating the observed energy

142 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

10:45 11:00 11:15 11:30 11:45 12:00 12:15 12:30 12:45 13:00 13:15

time

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05

Man

ning

s n

(s/m

1/3)

Analysis ensemble (real drifters), Aug 20 (channel)

ensemblemeaninitial estimate

Fig. 14. Ensemble (thin light red curves) and mean (thick red curve) estimates of Manning’s n in Katama Inlet from assimilating drifters in Edgartown Channel on August

20 as a function of time. The black line is the initial estimate n = 0 . 035 s/m

1 / 3 . (For interpretation of the references to colour in this figure legend, the reader is referred to

the web version of this article.)

Fig. 15. Kinetic energy versus time for observations (black curves), the model with no assimilation and n = 0 . 035 s/m

1 / 3 (dashed blue curves), and ensemble (thin light

red curves) and mean (thick red curve) estimates of n in the inlet from assimilating drifters within Edgartown Channel on August 20 versus time at each sensor location

(numbers on top of each panel refer to sensor locations in the map in Fig. 3 ). (For interpretation of the references to colour in this figure legend, the reader is referred to

the web version of this article.)

o

r

(

t

d

a

u

l

( Fig. 15 ). The model is initialized with n = 0 . 035 s/m

1 / 3 , and run

over the window from 12:00 to 1:10 pm ( Fig. 16 ).

In this case, the estimate of n oscillates and decreases initially,

and after 1 hr returns to the initial value of n = 0 . 035 s/m

1 / 3 (al-

though the ensemble may not have converged; Fig. 16 ). This is be-

cause the model is not consistently over- or under-estimating the

observed kinetic energy at the start of the window, and thus the

assimilated ensemble does not increase or decrease the estimate of

n by the end of the assimilation.

These results suggest that the assimilation outcome can depend

n the time and location of drifter deployment. Because the pa-

ameter of interest is the friction in a specific part of the domain

Katama Inlet), when drifters are deployed near or in that region,

he assimilation performs better. For the experiments with drifters

eployed in Edgartown Channel, the results depend on when the

ssimilation begins. This is linked to whether the model over- or

nder-estimates the kinetic energy at the beginning of the assimi-

ation window. Further experiments would help determine the rel-

L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144 143

time12:00 12:15 12:30 12:45 13:00 13:15

Man

ning

s n

(s/m

1/3)

0.015

0.02

0.025

0.03

0.035

0.04

0.045

0.05Analysis ensemble (real drifters), Aug 20 (channel); restart

ensemblemeaninitial estimate

Fig. 16. Ensemble (thin light red curves) and mean (thick red curve) estimates of Manning’s n in Katama Inlet from assimilating drifters in Edgartown Channel beginning at

12:00 pm on August 20 versus time. The black line is the initial estimate n = 0 . 035 s/m

1 / 3 . (For interpretation of the references to colour in this figure legend, the reader is

referred to the web version of this article.)

a

i

a

c

b

e

c

t

C

s

m

t

6

(

w

t

s

o

t

w

d

l

d

j

n

p

a

o

a

n

d

I

t

t

t

a

s

s

s

a

u

e

d

r

t

a

r

w

h

a

t

s

m

t

a

f

w

a

t

K

o

n

e

t

a

A

t

N

t

A

fi

A

t

(

fi

g

f

tive importance of drifter deployment location and the difference

n observed and simulated kinetic energy at the beginning of the

ssimilation window.

Note that these experiments do not include any covariance lo-

alization, a common method for reducing artificial correlations

etween spatially-distant regions of the domain, since the param-

ter of interest covers an entire subregion that may or may not in-

lude the drifter trajectories. Thus, these results demonstrate how

he assimilation behaves when drifter observations in Edgartown

hannel are allowed to update n in Katama Inlet without any con-

traints. Imposing localization in the Edgartown Channel experi-

ents would likely slow the time to convergence without changing

he overall behavior of the ensemble estimate of n .

. Conclusions

Trajectories of drifters are assimilated into a numerical model

ADCIRC) to estimate the friction (Manning’s n ) in Katama Inlet,

hich affects circulation in tidally-dominated Katama Bay. Syn-

hetic observation experiments demonstrate the ability of the as-

imilation method to estimate Manning’s n using only trajectories

f passive Lagrangian drifters. The performance of the assimila-

ion is greatest when the drifters are located near the region for

hich n is estimated. When the synthetic drifters are located in a

ifferent region (Edgartown Channel), away from the Katama In-

et region for which n is estimated, the assimilation performance

ecreases, likely owing to interactions between the intrinsic ad-

ustment time of the bay, sensitivity to observational noise, and

onlinear effects within the data assimilation method. This is sup-

orted by the investigations with identical setups but different re-

lizations of observational noise ( Section 4.3 ): the two realizations

f the Katama Inlet experiment were qualitatively indistinguish-

ble, while the two Edgartown Channel experiments differed sig-

ificantly.

There are larger differences in the outcomes when real drifter

ata are assimilated, depending on whether drifters from Katama

nlet or Edgartown Channel are assimilated. Assimilation of trajec-

ories observed from drifters released near Katama Inlet converges

o a larger inlet drag coefficient than the 2011 value. Throughout

he system, the corresponding simulated kinetic energy with the

ssimilated n is often closer to the observed kinetic energy than

imulations with the 2011 value. In contrast, when trajectories ob-

erved from drifters released in Edgartown Channel in 2013 are as-

imilated, n is reduced and the kinetic energy estimates are not as

ccurate. This is partially due to the mismatch between the sim-

lated (initialized with the 2011 value of n ) and observed kinetic

nergy at the beginning of the assimilation window, and partially

ue to the larger spatial distance between the observations and the

egion for which n is estimated. These results are also sensitive to

he time the drifters are released in the channel.

Differences in assimilation performance between the synthetic

nd real experiments are likely due to unmodeled processes in the

eal experiment that may have a larger effect on the assimilation

hen the observations are far from the region of interest, owing to

igher sensitivity to noise. Thus, an OSSE’s ability to provide guid-

nce decreases with increasing distance between observations and

he region of interest.

The initial numerical circulation model used bathymetry mea-

ured in 2013 and a parameter tuned for kinetic energy measure-

ents in 2011. The Katama Bay domain changed significantly in

he area of Katama Inlet between 2011 and 2013 (recall Fig. 1 B

nd C), and the goal was to improve the parameter estimate n

rom 2011 to represent the 2013 situation. Results depend on both

hen and where drifters are observed: if one wishes to estimate

local parameter in a model, then it is best to deploy drifters in

hat region. Ultimately, assimilation of real drifter trajectory data in

atama Inlet provides an improved estimate of n in the inlet, based

n comparisons between observed kinetic energy in 2013 and ki-

etic energy from the model simulations with the 2011 and 2013

stimates of the parameter. While Eulerian data are used to judge

he performance of the assimilation, they are not necessary for the

ctual computation of the parameter.

cknowledgments

This work was supported by: Department of Defense Mul-

idisciplinary University Research Initiative (MURI) [grant

0 0 0141110087], administered by the Office of Naval Research;

he National Science Foundation (NSF); the National Oceanic and

tmospheric Administration (NOAA); NOAA’s Climate Program Of-

ce; the Department of Energy’s Office for Science (BER); and the

ssistant Secretary of Defense (Research & Engineering). Drifter

echnology was developed out of Gulf of Mexico Research Initiative

GoMRI) support. The authors would also like to thank the PVLAB

eld crew for helping obtain the observations. Finally, the authors

ratefully acknowledge the helpful comments and suggestions

rom three anonymous reviewers.

144 L.C. Slivinski et al. / Ocean Modelling 113 (2017) 131–144

M

M

M

M

M

M

M

M

M

O

O

O

R

S

S

S

S

S

T

T

V

W

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